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Simplifying 52x(x + -7) = 43 Reorder the terms: 52x(-7 + x) = 43 (-7 * 52x + x * 52x) = 43 (-364x + 52x2) = 43 Solving -364x + 52x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + -364x + 52x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -364x + 52x2 = 0 Begin completing the square. Divide all terms by 52 the coefficient of the squared term: Divide each side by '52'. -0.8269230769 + -7x + x2 = 0 Move the constant term to the right: Add '0.8269230769' to each side of the equation. -0.8269230769 + -7x + 0.8269230769 + x2 = 0 + 0.8269230769 Reorder the terms: -0.8269230769 + 0.8269230769 + -7x + x2 = 0 + 0.8269230769 Combine like terms: -0.8269230769 + 0.8269230769 = 0.0000000000 0.0000000000 + -7x + x2 = 0 + 0.8269230769 -7x + x2 = 0 + 0.8269230769 Combine like terms: 0 + 0.8269230769 = 0.8269230769 -7x + x2 = 0.8269230769 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 0.8269230769 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 0.8269230769 + 12.25 Combine like terms: 0.8269230769 + 12.25 = 13.0769230769 12.25 + -7x + x2 = 13.0769230769 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 13.0769230769 Calculate the square root of the right side: 3.616202853 Break this problem into two subproblems by setting (x + -3.5) equal to 3.616202853 and -3.616202853.Subproblem 1
x + -3.5 = 3.616202853 Simplifying x + -3.5 = 3.616202853 Reorder the terms: -3.5 + x = 3.616202853 Solving -3.5 + x = 3.616202853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.616202853 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.616202853 + 3.5 x = 3.616202853 + 3.5 Combine like terms: 3.616202853 + 3.5 = 7.116202853 x = 7.116202853 Simplifying x = 7.116202853Subproblem 2
x + -3.5 = -3.616202853 Simplifying x + -3.5 = -3.616202853 Reorder the terms: -3.5 + x = -3.616202853 Solving -3.5 + x = -3.616202853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.616202853 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.616202853 + 3.5 x = -3.616202853 + 3.5 Combine like terms: -3.616202853 + 3.5 = -0.116202853 x = -0.116202853 Simplifying x = -0.116202853Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.116202853, -0.116202853}
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